Building competence.
WHAT THESE FIELDS SHARE
Mathematical foundations A substantial body of established knowledge A gap between understanding and doing
WHAT TO BUILD FIRST
The mathematics the field rests on.
WHAT THAT USUALLY MEANS
Linear algebra Probability and statistics Calculus Discrete mathematics, for some fields
WHY IT CANNOT BE SKIPPED
The literature assumes it, and progress stops without it.
WHAT TO DO ALONGSIDE
Build something, continuously.
WHY
Understanding a paper and implementing it are entirely different, and the gap is where learning happens.
WHAT TO READ
Textbooks, for foundations Survey papers, for orientation Recent papers, once oriented
WHAT TO BE CAREFUL WITH
Reading only recent work, without the foundations it assumes Following tutorials without understanding Confusing familiarity with capability
WHAT TO SEEK
Someone doing the work, who will look at yours.
WHAT TO CONTRIBUTE TO
Open projects in the field, which provide review and exposure.
WHAT TO EXPECT
Years, not months.
WHAT TO ACCEPT
That most of these fields have small communities, and reaching them requires deliberate effort.
